import random
import torch
from d2l import torch as d2l

def synthetic_data(w, b, num_examples):
    '''生成数据集: y=Xw+b+噪声'''
    X = torch.normal(0, 1, (num_examples, len(w)))
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape)
    return X, y.reshape((-1, 1))

true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)

d2l.set_figsize()
d2l.plt.scatter(features[:, (1)].detach().numpy(), labels.detach().numpy(), 1)

def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices)
    for i in range(0, num_examples, batch_size):
        batch_indices = torch.tensor(indices[i: min(i + batch_size, num_examples)])
        yield features[batch_indices], labels[batch_indices]

batch_size = 10
for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break

def linreg(X, w, b):
    '''线性回归模型'''
    return torch.matmul(X, w) + b

def squared_loss(y_hat, y):
    '''
        均方差损失函数
    '''
    return (y_hat - y.reshape(y_hat.shape)) **2 /2

def sgd(params, lr, batch_size):
    '''
        优化算法，小批量随机梯度下降
    '''
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad/ batch_size
            param.grad.zero_()

#学习率
lr = 0.03
num_epochs = 3
loss = squared_loss
for epoch in range(num_epochs):
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y)
        #
        l.sum().backward()
        #使用参数的梯度更新参数
        sgd([w, b], lr, batch_size)
    with torch.no_grad():
        